How did syn + ek + dekhesthai compound to signify 'synecdoche' (a figure of speech, in which a part is used for the whole)?

How do syn, ex-, dekhesthai appertain to the Modern English definition of synecdoche? I am baffled, because all 3 Greek morphemes are UNRELATED.

  1. ‘synecdoche’ doesn’t appertain to “with”, or any notion of togetherness. What does syn mean here?

  2. ‘synecdoche’ doesn’t appertain to outness or outwardness! What does ex- mean here?

  3. How’s dekhesthai (“to receive”) relevant to synecdoche? What do synecdoches receive? From what, where or whom do synecdoches receive?

University of Waterloo

Etymology

Gk. “to take with something else” or Gr. from sun “together with” and “a receiving from”

[Etymonline]

synecdoche (n.)

“figure of speech in which a part is taken for the whole or vice versa,” late 15c. correction of synodoches (late 14c.),
from Medieval Latin synodoche, alteration of Late Latin synecdoche,
from Greek synekdokhe “the putting of a whole for a part; an understanding one with another,” literally “a receiving together or jointly,”
from synekdekhesthai “supply a thought or word; take with something else, join in receiving,”
from syn- “with” (see [syn-] + ek “out” (see [ex-] + dekhesthai “to receive,” related to dokein “seem good” (from PIE root [*dek-] “to take, accept”).

Typically an attribute or adjunct substituted for the thing meant (“head” for “cattle,” “hands” for “workmen,” “wheels” for “automobile,” etc.).

Ekdoche in Ancient Greek has also the meaning of taking or understanding in a certain sense.